# P-adic-absolute-value meaning

(number theory, field theory) A norm for the rational numbers, with some prime number

*p*as parameter, such that any rational number of the form — where*a*,*b*, and*p*are coprime and*a*,*b*, and*k*are integers — is mapped to the rational number , and 0 is mapped to 0. (*Note:*any rational number, except 0, can be reduced to such a form.)According to Ostrowski's theorem, only three kinds of norms are possible for the set of real numbers: the trivial absolute value, the real absolute value, and the p-adic absolute value.WP.

noun

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